Exact Solutions and Numeration Program for Free Oscillation in Duffing Soft Spring System.

Exact Multiplicity for Periodic Solutions of Duffing type

In this paper, we study the following Duffing-type equation: x′′ + cx′ + g(t, x) = h(t), where g(t, x) is a 2π-periodic continuous function in t and concave-convex in x, and h(t) is a small continuous 2π-periodic function. The exact multiplicity and stability of periodic solutions are obtained.

EXACT SOLUTIONS FOR FLOW OF A SISKO FLUID IN PIPE

By means of He's homotopy perturbation method (HPM) an approximate solution of velocity eld is derived for the ow in straight pipes of non-Newtonian uid obeying the Sisko model. The nonlinear equations governing the ow in pipe are for- mulated and analyzed, using homotopy perturbation method due to He. Furthermore, the obtained solutions for velocity eld is graphically sketched...

Boundedness of solutions for semilinear duffing equations

The extended homogeneous balance method and exact solutions of the Maccari system

The extended homogeneous balance method is used to construct exact traveling wave solutions of the Maccari system, in which the homogeneous balance method is applied to solve the Riccati equation and the reduced nonlinear ordinary differential equation. Many exact traveling wave solutions of the Maccari system equation are successfully obtained.

Power Series -Aftertreatment Technique for Nonlinear Cubic Duffing and Double-Well Duffing Oscillators

Modeling of large amplitude of structures such as slender, flexible cantilever beam and fluid-structure resting on nonlinear elastic foundations or subjected to stretching effects often lead to strongly nonlinear models of Duffing equations which are not amendable to exact analytical methods. In this work, explicit analytical solutions to the large amplitude nonlinear oscillation systems of cub...